Hospitals would apply to be repaid for paying trauma surgeons to be on call and taking care of uninsured and underinsured patients.
Donoghue, whose subcommittee worked on the legislation, said he was pleased that the bill is headed to the House of Delegates next week.
It will keep the doors open at rural trauma centers, which were facing shutdowns as soon as this summer.
Last summer, Washington County Hospital closed its trauma center for four months because there weren't enough surgeons to staff it around the clock.
In order to reopen the trauma center, the hospital agreed to pay surgeons $1.7 million a year in on-call costs, which cannot be recovered through hospital rates.
"Washington County Hospital turned out to be the model for the state," Donoghue said.
The legislation would cost each of the state's 3.7 million drivers less than a penny a day. Drivers must renew their licenses every five years.
House Speaker Michael E. Busch, the bill's lead sponsor, had initially proposed a $2 per vehicle charge on insurance carriers.
The committee also rejected other financing options, including extra fines for drunk drivers.